Question

Elisa Test The standard test for the HIV virus is the Elisa test, which tests for the presence of HIV antibodies. If an individual does not have the HIV virus, the test will come back negative for the presence of HIV antibodies 99.8% of the time and will come back positive for the presence of HIV antibodies 0.2% of the time (a false positive). If an individual has the HIV virus, the test will come back positive 99.8% of the time and will come back negative 0.2% of the
time (a false negative). Approximately 0.7% of the world
population has the HIV virus.
(a) What is the probability that a randomly selected individual
has a test that comes back positive?
(b) What is the probability that a randomly selected individual
has the HIV virus if the test comes back positive?

Answer 1

Ans:

P(HIV)=0.007

P(negative/no HIV)=0.998

P(positive/no HIV)=1-0.998=0.002

P(positive/HIV)=0.998

a)

P(positive)=P(positive/HIV)*P(HIV)+P(positive/no HIV)*P(no HIV)

=0.998*0.007+0.002*(1-0.007)

=0.008972

b)

P(HIV/positive)=P(positive/HIV)*P(HIV)/P(positive)

=0.998*0.007/0.008972

=0.778645